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Full text of "Analytical Mechanics"

PERIODIC MOTION
315
Eliminating K and solving for g we get
(1)
Reversible pendulums which are made for the purpose of determining g are so constructed that the two periods are very nearly equal.    Therefore we can write p' = p + 5p?
and obtain
g       jyg-pg
g~  w D' (P + spy-- DP*
D'2 - D2
= 47T2
P2 (Df -D) + 2 PD'SP + >' (5P)2
25 +D/                r/^NO is neglected]
P2
D'-D   P 1         2D'
D'-D
(2)
The approximate expression which is given in equation (2) is better adapted for computing the value of g from experimental data than the more exact expression given in equation (1). This is due to the fact that (Df  D), which cannot be determined with a high degree of accuracy, enters into equation (1) as a factor, while it appears only in the correction term of equation (2). 245. Bifilar Pendulum.  A rigid body which is suspended by means of two parallel strings, as shown in Fig. 142, is called a bifilar pendulum.
rf
\
-D-i
X
FIG. 141.
When the body is given an angular displacement about a vertical axis through
See Appendix Ai.